How to Tackle RC Passages that Feel Both Informational and Persuasive

Remember that there are three types of GRE and GMAT passages: Informational (I), Informational with Opinion (I+), or Persuasive (P).

Informational with Opinion (I+) passages tend to confuse a lot of students. These passages are mostly informational (but not 100%!) The author gives a lot of facts about the topic, but he does give us a little bit of opinion! They are sort of the “middle ground” between passages that are very boring and passages that are all “fired up.”

This can be a challenge to recognize! Maybe an author says a theory is “overlooked,” or describes a group of politicians as “noble-hearted, yet ineffective.” Perhaps the entire passage is informational until the very last sentence, and the author then suggests that something is a “shame,” or “requires more public attention.” We know it’s not quite Persuasive, but it’s not completely bereft of emotion. That’s how you know it is I+!

Let’s look at an example of this type of passage. I highlighted some interesting keywords for us to notice:

Passage

The Gross Domestic Product (GDP), which measures the dollar value of finished goods and services produced by an economy during a given period, serves as the chief indicator of the economic well-being of the United States. The GDP assumes that the economic significance of goods and services lies solely in their price, and that these goods and services add to the national well-being, not because of any intrinsic value they may possess, but simply because they were produced and bought. Additionally, only those goods and services involved in monetary transactions are included in the GDP. Thus, the GDP ignores the economic utility of such things as a clean environment and cohesive families and communities. It is therefore not merely coincidental, since national policies in capitalist and non-capitalist countries alike are dependent on indicators such as the GDP, that both the environment and the social structure have been eroded in recent decades. Not only does the GDP mask this erosion, it can actually portray it as an economic gain: an oil spill off a coastal region “adds” to the GDP because it generates commercial activity. In short, the nation’s central measure of economic well-being works like a calculating machine that adds but cannot subtract.

Analysis

There’s at least three places in which the author gives a clear opinion, although I suppose “mask” is not particularly opinionated. Since this passage has an opinion, but doesn’t contain 3 super-strong sentences of opinion, we would probably want to error on the side of caution and classify it as “Informational +”. That means the Main Idea should be opinionated, but not be TOO extreme. We need a good “middle ground” answer choice. Our Test-Day notes might look like this:

POV: GDP 🙁
P: I+ (to give info + opinion)

Let’s look at the “Main Idea” question. This is a wordy one, so let’s scan through them, and examine the verbs first:

Question

The primary purpose of the passage is to:

(A) identify ways in which the GDP could be modified so that it would serve as a more accurate indicator of the economic well-being of the United States

(B) suggest that the GDP, in spite of certain shortcomings, is still the most reliable indicator of the economic well-being of the United States

(C) examine crucial shortcomings of the GDP as an indicator of the economic well-being of the United States

(D) argue that the growth of the United States economy in recent decades has diminished the effectiveness of the GDP as an indicator of the nation’s economic well-being

(E) discuss how the GDP came to be used as the primary indicator of the economic well-being of the United States

 

Verbs-only:

(A) identify… (B) suggest… (C) examine… (D) argue… (E) discuss…

 

——

We want a “middle-of-the-road” verb — something that isn’t too Persuasive, but isn’t 100% dry and Informational. Notice how in this group of verbs, (D) is by far the strongest. Does it make sense for the strongest verb to be correct, when we know this isn’t a full-blown Persuasive passage? Nope! So we can eliminate (D).

Of the four that are left, (E) is the most casual and Informational. To “discuss” something is pretty innocuous and un-opinionated, so unless the second-half says something such as, “to discuss why the GDP isn’t that great,” we can tell this isn’t going to be the correct answer.

The only verbs in the running for a “middle-of-the-road” answer choice, a choice that has some opinion, but not too much opinion, are (A), (B), and (C). Let’s look at them in full context again. Notice how even the answer choices reveal specific tones and points of view:

(A) identify ways in which the GDP could be modified so that it would serve as a more accurate indicator of the economic well-being of the United States

(B) suggest that the GDP, in spite of certain shortcomings, is still the most reliable indicator of the economic well-being of the United States

(C) examine crucial shortcomings of the GDP as an indicator of the economic well-being of the United States

——

Notice how (B) is very positive towards the GDP, whereas (A) and (C) are more negative. Again, since the correct answer and the “second-best” are often very close together, this is a good indicator that the correct answer lies between (A) and (C). Also, it helps we identified the keywords and know the author has some reservations about the GDP.

Let’s look at our “Final Two”:

(A) identify ways in which the GDP could be modified so that it would serve as a more accurate indicator of the economic well-being of the United States

(C) examine crucial shortcomings of the GDP as an indicator of the economic well-being of the United States

This is purely a choice in regards to Tone. Does the author think we can “fix” the GDP so it is more accurate, or is the GDP inherently problematic?

Let’s look one more time at those opinionated sections above!

They are all negative about the GDP!

The author isn’t implying that the GDP is beneficial, so (A) incorrectly assumes the GDP is at least somewhat accurate, and that the main criticism is that it needs to be MORE accurate. This choice is very tricky, and implies the author gives some praise to the GDP as a measuring tool of economic well-being. No such praise is in the passage. Like many passages, the tone is negative and fairly critical throughout.

The correct answer is (C) because it best fits the tone of the ENTIRE passage. (A) contains a tone of praise that is not present in the passage. This passage is a little tricky, but you can see that if you wanted to pick (A), you would need to identify a sentence in which the author says something good about the GDP. But where is that in the passage? Nowhere!

How to Attack Tough GRE Text Completions

black and white blackboard business chalkboard

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Let’s look at a harder Text Completions problem!

The simplicity of the theory—its main attraction is also its (i) _____, for only by (ii) _____the assumptions of the theory is it possible to explain the most recent observations made by researchers.

A liability.. accepting

B virtue.. qualifying

C downfall.. considering

D glory.. rejecting

E undoing.. supplementing

For Text Completions, remember that strategically we want to break down the original sentence and fill in the blanks with our own words/phrases prior to looking at the answer choices. The reason to do this isn’t ONLY in the hopes that the correct answer will perfectly match our prediction (although that’s always nice when it happens!), but we want to spend more time noticing the specific keywords in the sentence.

This is because usually the difference between the correct answer in TC and the 2nd best choice, is that the correct answer’s words fit the context of the original sentence/s just a little bit better.

The reason most people pick the “2nd best” choice, is because they didn’t spend enough time looking at that context. Now of course we don’t want to spend 5 min staring at this sentence, but you will know that your Text Completion strategy is weak if you don’t write anything down when you read the sentence/s and just try to do it all in your head.

So, for this one, let’s look at what we’re given. I’m going to bold some of the words that really stand out to me:

The simplicity of the theory—its main attraction is also its (i) _____, for only by (ii) _____the assumptions of the theory is it possible to explain the most recent observations made by researchers.

The author says this theory has “simplicity.” What does that mean? Well, it’s not complex. There’s some sort of simple explanation for it. He goes on to say that the “attraction” of the theory is also something else. “Attraction” is a positive word, so the 1st blank could be something positive as well, or something negative. Let’s look at how those meanings might sound:

The theory’s main attraction is also its SUPER POSITIVE THING.

or

The theory’s main attraction is also its SUPER NEGATIVE THING.

The 2nd meaning is more likely, because perhaps by “simplicity” the author means “irony.” That the main attractive quality of the theory is also it’s Achilles’ heel?

So, for the first blank, I am going to predict words like that:

(i) Achilles’ heel, downfall, thing that repels people

At this point, if you were struggling to predict for the 2nd blank, you would still be able to eliminate answer choices (B) and (D), since “virtue” and “glory” are positive things.

But let’s push ourselves to predict for the 2nd blank as much as can!

The simplicity of the theory—its main attraction is also its NEGATIVE THING, for only by (ii) _____the assumptions of the theory is it possible to explain the most recent observations made by researchers.

The phrase “for only” implies that the 2nd part will explain how its main attractive is also negative. “Assumptions” are a negative thing. We don’t like to make assumptions about people!

Let’s try out a positive word, a neutral word, and a negative word here:

  1. for only by BELIEVING (+) the assumptions of the theory is it possible to explain the most recent observations

  2. for only by PROVIDING (neutral) the assumptions of the theory is it possible to explain the most recent observations

  3. for only by IGNORING (-) the assumptions of the theory is it possible to explain the most recent observations

Since “possible to explain” is a positive thing, it makes the most sense that we would want something overall negative here. Words like “believing” don’t really make sense in context.

So, let’s go back to (A), (C), and (E) are look for something that shows we need to show those assumptions are negative.

(A) accept the assumptions

(C) considering the assumptions (this is pretty neutral) …we’re missing that sense of irony

(E) supplementing the assumptions

Therefore, (E) has to be the correct answer.

Reading it back, the meaning is:

People like the theory because it is SIMPLE, but that is also its UNDOING, because we have to ADD TO IT (SUPPLEMENT) to make it work!

SC Drill: Ten Questions that Test Meaning

man wearing black crew neck shirt reading book

Photo by Oladimeji Ajegbile on Pexels.com

Set a timer for 20 minutes, and try these ten SC questions. When you’re done, you can find the explanations on Google on GMATClub! 🙂

1) Minerva Consulting has a budget about the same as the largest consulting firms in the state, like Cost Stonehouse or McKidney’s, but only twenty four in workforce, all of whom have advanced degrees.

(A) about the same as the largest consulting firms in the state, like Cost Stonehouse or McKidney’s, but only twenty four in workforce, all of whom have

(B) of about the same as the largest consulting firms in the state have, as Cost Stonehouse or McKidney’s, but in Minerva there is only a workforce of twenty four, and all of them have

(C) that is about the same as the budgets of largest consulting firms in the state, such as Cost Stonehouse or McKidney’s, but in Minerva with a workforce of only twenty four, all of them having

(D) comparable to the budgets of the largest consulting firms in the state, like Cost Stonehouse or McKidney’s, but only twenty four in workforce, and all have

(E) comparable to those of the largest consulting firms in the state, such as Cost Stonehouse or McKidney’s, but a workforce of only twenty four, all of whom have

 

2) Quintus Flaccus (65 – 8 BCE), known in the English-speaking world as “Horace”, was a contemporary of Virgil and the preeminent lyrical poet of the Augustan age; his poems were known as the “common currency of civilization” because they were so widely read and quoted, and over the past two millennia have had a much greater influence than any poet from ancient Rome.

(A) than any

(B) than any other

(C) as any other

(D) as those of any other

(E) than those of any other

 

3) The state of Maine, in the extreme northeast corner of the continental United States, shares land borders with two Canadian provinces, Quebec and New Brunswick, but only is adjacent with one state, New Hampshire

(A) only is adjacent with one

(B) is adjacent only with one

(C) is adjacent to only one other

(D) only is adjacent to one

(E) is only adjacent to one other

 

4) Geophysically, Eurasia is Earth’s largest landmass, and their peaks, the Himalayas, are the highest corresponding mountains on Earth.

(A) their peaks, the Himalayas, are the highest corresponding

(B) its peaks, the Himalayas, are correspondingly the highest

(C) its peaks, the Himalayas, are the highest corresponding

(D) its peaks, the Himalayas, correspond to the highest

(E) their peaks, the Himalayas, are correspondingly the highest

 

5) By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, in 1797–1798 Henry Cavendish’s apparatus enabled him to arrive at an astonishingly accurate figure for the weight of the earth.

A. By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, in 1797–1798 Henry Cavendish’s apparatus enabled him

B. In 1797–1798, by devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, Henry Cavendish’s apparatus enabled him

C. Henry Cavendish devised an instrument made from a rod, wire, and lead balls, and employed uncommonly precise measurements, and in 1797–1798 was able

D. Having devised an instrument from a rod, wire, and lead balls, and employment of uncommonly precise measurements, Henry Cavendish in 1797–1798 was able

E. By devising an instrument made from a rod, wire, and lead balls, and employing uncommonly precise measurements, Henry Cavendish was able in 1797–1798

 

6) Even-toed ungulates, including pigs, cattle, goats, and sheep, and odd-toed ungulates, such as horses and donkeys, account for all the mammals domesticated for agricultural purposes.

(A) including pigs, cattle, goats, and sheep, and odd-toed ungulates, such as horses and donkeys, account for

(B) including pigs, cattle, goats, and sheep, and odd-toed ungulates, including horses and donkeys, accounting for

(C) included among pigs, cattle, goats, and sheep, and odd-toed ungulates, such as horses and donkeys, account for

(D) included among pigs, cattle, goats, and sheep, and odd-toed ungulates, like horses and donkeys, are accounted for by

(E) like pigs, cattle, goats, and sheep, and odd-toed ungulates, like horses and donkeys, are accounted for by

 

7) While the marketing department projected robust sales throughout the summer, typically Allport Corporation’s biggest season, the drought in Midwestern states limited total revenue to only $300 million in the third quarter.

(A) typically Allport Corporation’s biggest season, the drought in Midwestern states limited total revenue to only

(B) Allport Corporation’s biggest typical season, the drought in Midwestern states limited only total revenue to

(C) which typically is Allport Corporation’s biggest season, the drought in Midwestern states only limited total revenue to

(D) which is typically Allport Corporation’s biggest season, the drought in Midwestern states limiting total revenue to only

(E) Allport Corporation’s biggest typical season, the drought in Midwestern states only limiting total revenue to

 

8) After establishing several lucrative deals in the Far East, the CEO of Brantford Industrial said that he wanted to encourage their expanding into promising overseas markets, the use of domestic suppliers for all materials besides oil products, and the acquisition of a more extensive distribution network.

(A) their expanding into promising overseas markets, the use of domestic suppliers for all materials besides

(B) their expansion into promising overseas markets, using domestic suppliers for all materials instead of

(C) its expansion into promising overseas markets, the use of domestic suppliers for all materials other than

(D) its expansion into promising overseas markets, using domestic suppliers for all materials other than

(E) its expanding into promising overseas markets, using domestic suppliers for all materials except

 

9) Daniel Bernoulli derived the famous fluid equation named after him, to explain an airplane’s wing’s generation of lift, and made a discovery that led to an early method of measuring blood pressure.

(A) equation named after him, to explain an airplane’s wing’s generation of lift

(B) equation named after him, and this principle explains the lift of an airplane’s wing

(C) equation, named it after himself, explained how an airplane’s wing is generating lift

(D) equation named for him, giving an explanation of the generation of the lift of an airplane’s wing

(E) equation named for him, which explains how an airplane’s wing generates lift

 

10) Based on records from ancient Athens, each year young Athenian women collaborated to weave a new woolen robe that they used to dress a statue of the goddess Athena and that this robe depicted scenes of a battle between Zeus, Athena’s father, and giants.

(A) Based on records from ancient Athens, each year young Athenian women collaborated to weave a new woolen robe that they used to dress

(B) Based on records from ancient Athens, each year young Athenian women had collaborated to weave a new woolen robe with which to dress

(C) According to records from ancient Athens, each year young Athenian women collaborated to weave a new woolen robe that they used to dress

(D) Records from ancient Athens indicate that each year young Athenian women collaborated to weave a new woolen robe with which they dressed

(E) Records from ancient Athens indicate each year young Athenian women had collaborated to weave a new woolen robe for dressing 

700+ Level: Practicing Geometry Word Problems

nbc jack chalkboard referenceAlgebraic translation (turning the description of relationships between x and y, apples and oranges, Todd’s income to Sarah’s income, perimeter to area, etc.) is a fundamental GMAT skill. Some students see this skill as a “trap” or some kind of nightmare. 😉

The truth is, you cannot avoid Problem Solving word problems on Test Day. BUT…you can conquer your fear of them by practicing specific types of Word Problems to hone particular skills. It’s always better to focus on one area at a time and build up your skill-set that way than do a million mixed Word Problems all at once.

Remember, word smarter, not harder!

Below are two GMAT questions that involve Geometry. Students get particularly frustrated with questions like these because Geometry is so inherently visual. When the GMAT doesn’t provide us with the diagram or image, we feel cheated. 😉

“What?! You mean I have to draw something AND come up with my own equations for it!”

These problems are especially good practice for anyone looking to break a Q40 or boost their Geometry abilities. Before you tackle these problems, you may want to read through my Reddit post of these types of questions.

Ready to go? Set a timer for 5 minutes, and see if you can get through both of them!

Question #1

A rectangular park has a perimeter of 340 feet and a diagonal measurement of 130 feet.What is its area, in square feet?

(A) 2500

(B) 1440

(C) 6000

(D) 7040

(E) 8080

Question #2

2017-11-07_0941

The above figure represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 18

 

Scroll down for explanations!

 

 

 

 

 

EXPLANATIONS

Question #1

Let x and y equal the length and width of the rectangle. The perimeter is 340.

2x+2y=340

x+y=170

The diagnonal is 130.

x^2 + y^2 = 130^2

We want to find the value of xy, so let’s square both sides of the first equation to make it look like the second:

x^2 + 2xy + y^2 = 170^2

We can substitute 130^2 in for x^2 + y^2 in the second equation:

2xy + 130^2 = 170^2

2xy = 170^2 – 130^2

The right-hand side of our equation looks like our common Quadratic x^2 – y^2 = (x + y)(x – y).

2xy = (170 + 130)(170 – 130)

2xy = (300)(40)

xy = (300)(20)

xy = 6000

The correct answer is (C).

Question #2

We can say that the length of the rectangle is x – 4, and that the width is x – 6.

Area = (x-4)(x-6) = 48
x = 12

The correct answer is (C).

Here’s similar questions on GMATClub that you may want to practice:

Rectangular Yard + Hedge Question

Border and Photograph Question

Ratios with Brass Inlay Question

Modifiers and Meaning in Sentence Correction

Let’s look at a Sentence Correction question that seems rather challenging at first:

Instead of buying stocks and bonds, which are the conventional approach for someone new to financial planning, real estate has become increasingly the choice of young people as a first investment.

A) buying stocks and bonds, which are the conventional approach for someone new to financial planning, real estate has become increasingly the choice of young people

B) buying stocks and bonds, which are the conventional approach for those new to financial planning, increasingly young people have shown a choice for real estate

C) buying stocks and bonds, which are the conventional approach for someone new to financial planning, the choice of young people increasingly has become real estate

D) buying stocks and bonds, which are the conventional investments for those new to financial planning, young people have increasingly chosen real estate

E) stocks and bonds, which are the conventional approach for those new to financial planning, young people have shown an increasing choice of real estate

This question is almost completely underlined, and many students get nervous when they see these. But fear not! What appears super-challenging at first, might actually be more straightforward than we think if we mentally delete the “which are…” modifier in the middle of the sentence.

It’s always nice when a long sentence openings with an -ing modifer like this, because then you can skip ahead to the comma to make sure that whatever follows can logically perform that action.

(A) “real estate” cannot “buy” stocks and bonds. Eliminate.
(B) “young people” could “buy” stocks and bonds. Keep.
(C) “the choice” cannot “buy” stocks and bonds. Eliminate.
(D) “young people” can “buy” stocks and bonds. Keep.
(E) different construction…Keep for now.

In (B), the adverb “increasingly” is oddly placed in front of the noun “young people.” Normally, I wouldn’t eliminate for something so petty, but (D) and (E) gives us two better choices, so you can assume the correct answer lies with them.

Let’s look at our Final Two and highlight the differences:

D) Instead of buying stocks and bonds, which are the conventional investments for those new to financial planning, young people have increasingly chosen real estate

E) Instead of stocks and bonds, which are the conventional approach for those new to financial planning, young people have shown an increasing choice of real estate

(E) is wordier and more awkward, but more important has a noun-verb issue. “Approach” is singular, but “stocks and bonds” are plural, and the sentence is using the plural “are.”

It has to be (D). Notice how (D) nicely places the adverb “increasingly” right next to its verb. This what the GMAT prefers, if possible. Modifiers are nice when they touch! :)

GMAT SC: The Myth of “Intended Meaning”

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Joan of Arc…preparing for the GMAT exam

Sometimes I read explanations for GMAT Sentence Correction questions that state something like this: “Choice X cannot be the correct answer because it changes the meaning of the original sentence,” or, “Choice Y cannot be right, because it is not the intended meaning of the sentence.”

Let’s be clear: there is no such thing as “original” or “intended” meaning on the GMAT. 

Any answer choice can be correct in Sentence Correction as long as it offers a sentence that is clear of grammar errors and makes logical real-world sense. If choice (A) offers a meaning that does not make logical sense, then it cannot be the correct answer. Choice (D) may offer a different meaning than (A) and be correct, because it corrects the meaning error in (A). It is not healthy for GMAT students to give the “(A) sentence” more weight, gravitas, or benefit of the doubt when it comes to meaning, simply because that sentence happens to occupy the first position in the question. (A)’s meaning is not any more likely to be correct or logical than (B)’s, (C)’s, (D)’s, or (E)’s. In order to step up your SC game, make sure you do not give (A) unnecessary value over the other options.

As for “intended,” what the GMAT intends is for the student to select an answer choice with a logical meaning. If that is (A), then great! If that is (B), then great! Just because (B)’s meaning is different than (A)’s, doesn’t mean (B) is automatically wrong.

In order to illustrate this point, let’s look at this question from the GMAT Official Guide:

Joan of Arc, a young Frenchwoman who claimed to be divinely inspired, turned the tide of English victories in her country by liberating the city of Orleans and she persuaded Charles VII of France to claim his throne.

Before we look at the answer choices, let’s remove the unnecessary modifiers and strip this long sentence down to its simple meaning:

Joan turned the tide by liberating AND she persuaded Charles to claim his throne.

Here we have the marker “and” separating two clauses. This is an indication we should check for Parallelism. We know the GMAT loves verbs to be parallel, so let’s highlight the verbs in the sentence that could be parallel.

Joan turned the tide by liberating AND she persuaded Charles to claim his throne.

We are faced with a decision. Is “persuaded” supposed to be parallel with “turned,” or is it supposed to be parallel with “liberating”? Often the logical meaning of the sentence will only make sense with ONE version, so let’s examine how the sentence would sound both ways:

Joan turned the tide by liberating AND persuaded Charles to claim his throne.

In this version, Joan is doing two separate actions: turning the tide, and persuading Charles.

Joan turned the tide by liberating AND persuading Charles to claim his throne.

In this version, Joan is only doing one action: turning the tide, and she is using two methods to help her turn the tide: she is (1) liberating the town, and she is (2) persuading Charles to claim his throne.

Here’s the difficulty with this question: either meaning is logical, and could be correct!!! If we read (A), and assumed that just because it said “persuaded,” then it HAS to be parallel with “turned,” we would be missing the nuance. We cannot eliminate (A) based on meaning, so let’s look at Parallelism.

Whether the Parallelism is turned/persuaded, or liberating/persuading, we know (because of our parallelism grammar rules), that the word “she” should not precede “persuaded” since it is unnecessary for the parallelism. Therefore, (A) is out.

Now let’s look at the other choices:

(B) persuaded Charles VII of France in claiming his throne
(C) persuading that the throne be claimed by Charles VII of France
(D) persuaded Charles VII of France to claim his throne
(E) persuading that Charles VII of France should claim the throne

The “that” in (C) and (E) breaks the paralllelism, since “liberating THE CITY” is not parallel with “persuading THAT….” If we had had the word “that” after liberating, then perhaps one of these two options could have been correct.

Now we’re on to our final two options:

(B) persuaded Charles VII of France in claiming his throne
(D) persuaded Charles VII of France to claim his throne

We now see that the correct meaning is the turned/persuaded Parallelism, so Joan did two distinct actions. Here, the only difference is the preposition preceding the verb “claiming/claim.”

Two questions must be asked:

(1) when faced with a 2nd verb (“persuaded” being the 1st verb), does the GMAT stylistically prefer the INFINITIVE form (“to claim”), or the PARTICIPLE form (“claiming”)?

(2) what is the correct preposition, idiomatically, to use with the verb “persuaded”? do we say “persuaded in” or “persuaded to”?

The GMAT prefers the infinitive form, and the correct idiom is “persuaded to.” For both of these reasons, the correct answer is (D).

Takeaways:

  • There is no such thing as “intended” meaning. Ask yourself: does each sentence make real-world sense on its own, yes or no? If no, get rid of it.
  • The correct answer can have a slightly different meaning than the meaning presented in (A).
  • (A) is not “special,” or any more likely to be correct than (B), (C), (D), or (E). Let’s not give it unusual credence, or get SC questions wrong because we second-guessed our instincts.

 

Factorials (!) and Divisibility

exclamationIt’s amazing how something as simple as a (!) symbol can throw us all for a loop, even when really we’re just looking at a very simple divisibility question. This is my own question designed to mimic a GMATPrep question.

Start by setting a timer for 2-minutes and try this one on your own, then scroll down for the explanation!

Which of the following is an integer?

I. 10! / 3!
II. 9! / 8!
III. 13! / 11! 5!

A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Explanation:

If the result of a fraction is an integer that means that what is in the denominator divides evenly into what is in the numerator. The question for each of these Roman numerals becomes: will the denominator go evenly into the numerator?

Since we know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, and 3! = 3 x 2 x 1, it is obvious that the denominator of Roman Numeral 1 will go evenly into its numerator.

This same logic can be applied with Roman Numeral 2. As long as the factorial in the numerator is larger than the factorial in the denominator, then we will get a resulting integer.

Roman Numeral 3 is more complex. If we start by cancelling out the 11! from both the numerator and the denominator, the resulting fraction becomes:

(13 x 12) / (5 x 4 x 3 x 2)

Since 4 x 3 = 12, we can cancel those values out:
13 / (5 x 2)

Now we are stuck. 13 is a prime number, so neither 5 nor 2 will divide evenly into it. The result will be a decimal.

The correct answer is (D).